Concentration and cavitation phenomena of Riemann solutions for the isentropic Euler system with the logarithmic equation of state

The analytical solutions of the Riemann problem for the isentropic Euler system with the logarithmic equation of state are derived explicitly for all the five different cases. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 53; p. 103068
Main Author Sun, Meina
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Ltd 01.06.2020
Elsevier BV
Subjects
Cavitation
Convergence
Delta shock wave
Equations of state
Exact solutions
Isentropic Euler system
Logarithmic equation of state
Rarefaction
Riemann problem
Shock waves
Vacuum state
Logarithmic equation of state
Delta shock wave
Isentropic Euler system
Riemann problem
Vacuum state
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Summary:The analytical solutions of the Riemann problem for the isentropic Euler system with the logarithmic equation of state are derived explicitly for all the five different cases. The concentration and cavitation phenomena are observed and analyzed during the process of vanishing pressure in the Riemann solutions. It is shown that the solution consisting of two shock waves converges to a delta shock wave solution as well as the solution consisting of two rarefaction waves converges to a solution consisting of four contact discontinuities together with vacuum states with three different virtual velocities in the limiting situation.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2019.103068